Solvability of Nonlinear Difference Equations of Fourth Order
نویسنده
چکیده
In this article we show the existence of solutions to the nonlinear difference equation xn = xn−3xn−4 xn−1(an + bnxn−2xn−3xn−4) , n ∈ N0, where the sequences (an)n∈N0 and (bn)n∈N0 , and initial the values x−j , j = 1, 4, are real numbers. Also we find the set of initial values for which solutions are undefinable when an 6= 0 and bn 6= 0 for every n ∈ N0. When these two sequences are constant, we describe the long-term behavior of the solutions in detail.
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